Question 1: The sum of two numbers is and their difference is . Find the numbers.

Answer:

Let the two numbers be

Add (i) and (ii)

Therefore

Hence the two numbers are

Question 2: Twice a number is equal to thrice the other number. If the sum of the numbers is , find the numbers.

Answer:

Let the two numbers are

Solving for

or

Therefore

Hence the two numbers are .

Question 3: Find two numbers such that twice the first added to thrice the second gives and twice the second added to thrice the first gives .

Answer:

Let the numbers be

Solving for

Multiply i) by 2 and ii) by 3 and subtract ii) from i)

Substituting in i)

Hence the two numbers are

Question 4: Find two numbers which differ by and are such that four times the larger added to three times the smaller gives .

Answer:

Let the numbers be

Solving by

Multiply i) by 4 and subtract ii) from i)

Calculating for

Hence the two numbers are

Question 5: The sum of two numbers is and the difference of their squares is . Find the numbers.

Answer:

Let the two numbers be

Simplifying ii)

Solving for

Add i) and iii)

Substituting in i)

Hence the numbers are

Question 6: The sum of the digits of a two-digit number is . On adding to the number, its digits are reversed. Find the number.

Answer:

Let the two digit numbers be

Simplifying ii)

Solving for

Add i) and iii)

Substituting in i)

Hence the numbers is

Question 7: Two digit number is three times the sum of its digits. lf is added to the number, its digits are reversed. Find the original number.

Answer:

Let the two digit numbers be

Simplifying i) and ii)

Solving for

Multiplying iv) by 7 and Subtract iv) from ii)

Hence

Therefore the numbers is

Question 8: A two-digit number is seven times the sum of its digits. If is subtracted from the number, its digits get interchanged. Find the number.

Answer:

Let the two digit number be

Solving for

Multiplying ii) by 3 and Subtract ii) from i)

Hence

Therefore the numbers is

Question 9: Find a fraction which reduces to when is added to both its numerator and denominator; and reduces to when is added to both its numerator and denominator.

Answer:

Let the fraction be

Solving for

Multiplying i) by 5 and ii) by 3 and subtract ii) from i)

Hence

Therefore the fraction is

Question 10: On adding to the numerator of a fraction, it becomes . Also, on adding to the denominator of the original fraction, it becomes . Find the original fraction.

Answer:

Let the fraction be

Solving for

Multiplying i) by 3 and ii) by 2 and subtract ii) from i)

Hence

Therefore the fraction is

Question 11: In a given fraction, if the numerator is multiplied by and the denominator is reduced by , we get . But, if the numerator of the given fraction is increased by and the denominator is doubled, we get . Find the fraction.

Answer:

Let the fraction be

Solving for

Multiplying ii) by 2 and subtract ii) from i

Hence

Therefore the fraction in

Question 12: years ago, a lady was thrice as old as her daughter. years hence, the lady would be twice as old as her daughter. What are their present ages?

Answer:

Let the present age of lady

Let the Present age of Daughter

Solving for

Subtract ii) from i)

Hence

Therefore :

Lady’s Age

Daughter’s Age

Question 13: The sum of the ages of A and B is years. In years’ time, the age of A will be twice the age of B. Find their present ages.

Answer:

Let A’s Age

Let B’s Age

Solving for

Subtract ii) from i)

or

Therefore

A’s Age

B’s Age

Question 14: A is years elder than B. years ago A was four times as old as B. Find their present ages.

Answer:

Let the age of B

Hence A’s Age

Therefore

B’s Age

A’s Age

Question 15: Six years ago, the ages of Geeta and Seema were in the ratio . Nine years hence, their ages will be in the ratio . Find their present ages.

Answer:

Let the age of Geeta

Let the age of Seema

Solving for

Multiplying i) by 7 and ii) by 4 and Subtract ii) from i)

Hence

Therefore

Geeta’s Age

Seema’s Age

Question 16: knives and forks cost Rs. , while knives and, forks together cost Rs. . Find the cost of a knife and that of a fork.

Answer:

Let the cost of knives

Let the Cost of fork

Solving for

Multiplying i) by 3 and ii) 2

Hence

Hence Cost of :

Knive

Fork

Question 17: The cost of cups and spoons is Rs. , while the cost of cups and spoons is Rs. . Find the cost of cups and spoons.

Answer:

Let the cost of Cup

Let the Cost of Spoon

Solve for

Multiply i) by 16 and ii) by 13 and subtract ii) from i)

Hence

Hence Cost of:

Cup

Spoon

Question 18: Rahul covered a distance of km in hours, partly on bicycle at kmph and partly on moped at kmph. How much distance did he cover on moped?

Answer:

Total Distance

Total Time

Let the distance covered by cycle

Let the Distance covered by moped

Simplify

Hence Distance Covered by:

Cycle

Moped

Question 19: A boat can go km downstream in hours and, km upstream in hours. Find i) the speed of the boat in still water (ii) the rate of the current.

Answer:

Let the Speed of boat in still water

Speed of Stream

Solve for , add i) and ii)

Speed of Stream

Question 20: The monthly incomes of A and B are in the ratio and their monthly savings are in the ratio . If each spends Rs. per month, find the monthly income of each.

Answer:

Let A’s Income

Let B’s Income

Substituting

Hence

Therefore :

A’s Income

B’s Income

Question 21: nuts and bolts weigh grams, while nuts and bolts weigh grams. Find the weight of each nut and that of each bolt. How much do nuts and bolts weigh together?

Answer:

Let the Weight of Nut

Let the Height of Bolt

Solving for

Multiply i) by 8 and ii) by 6 and Subtract ii) from i)

Hence

Weight of:

Nut

Bolt

Therefore 3 Nuts and 3 Bolts will weight

Question 22: There are some girls in two classrooms, A and B. If girls are sent from room A to room B, the number of girls in both the rooms will become equal. If girls are sent from room B to room A, then the number of girls in room A would be double the number of girls in room B. How many girls are there in each class room?

Answer:

Let No. of girls in classroom

Solving ,

Subtract ii) from i)

Hence

No. of Girls in Class Room:

Question 23: men and boys can do a piece of work in days, while men and boys can finish it in days. How long would it take man alone to do it?

Answer:

Suppose 1 man finished the work in days and 1 Boy finished the work in days

There 1 man’s 1 day’s

And, 1 Boy’s 1 Day’s work

Now 4 men and 4 Boys finished the work in 3 days

Similarly 2 men and 5 boys finished in 4 days

Solving for

Multiply ii) by 2 and Subtract ii) from 2

or

Similarly

So one men can finished the work in

Question 24: A takes hours longer than B to walk km. But, if A doubles his pace, he is ahead of B by hour minutes. Find the speeds of A and B.

Answer:

Let the Speed of A

Let the Speed of B

Time taken By A

Time Taken By B

If A Double him Race Time taken by A

Therefore

Hence

Question 25: If the length of a rectangle is reduced by m and breadth increased by m, its area increases by m2. If however, the length is increased by m and breadth reduced by m, then the area is reduced by m2. Find the length and breadth of the rectangle.

Answer:

Let the Length of the rectangle

Let the Breadth of the rectangle

Solving for

From i)

Substituting in ii)

Hence

Therefore:

Length

Breadth

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Love that font 🙂

Cambria Math